A display device of the type described above is known from U.S. Pat. No. 4,822,144. In one of the examples shown in this patent, a pattern of phosphors is excited by UV radiation via an LCD switch. Notably when the luminescent layers in said example are transparent (organic) phosphors, waveguiding may occur in these layers due to reflection on the interfaces with, for example, the substrate or a transparent protective coating in such a layer. The same applies to layers of electroluminescent material forming, for example, an (O)LED or (Organic)Light-Emitting Device. Due to said waveguiding, much of the light generated in the layers is lost. Another consequence is that the light leaves the layers at undesired areas in the viewing direction, so that, for example, colors are mixed. Moreover, the layer of luminescent material is often coated with a transparent protective coating. Daylight is reflected on each of the layers (the substrate, the layer of luminescent material and the transparent protective coating), which is at the expense of the contrast.